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Use Property 8 to estimate the value of the integral.

$ \displaystyle \int^3_0 \frac{1}{x + 4} \,dx $

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00:42

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Use Property 8 to estimate…

0:00

Use Property 8 of integral…

00:35

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06:46

01:09

because of the fact that one over X plus four is decreasing on the interval. We know that 1/7 is less than one over X plus four, which is less than or equal to one for. Therefore, we know 17 times three months here, which is 3/7 is less than equal to the integral from 0 to 3 one over X plus four DX, which is less than or equal to 14 times three minutes here, which just 1/4 times three, which is simply 3/4.

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